Both Nikon P300 and Fujifilm XQ1 have 12.0 MP resolution sensors but Nikon P300's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Fujifilm XQ1's sensor is 2/3-inch (8.8 x 6.6 mm ).
Since Fujifilm XQ1's has a larger sensor area with the same resolution, this means that it also has a larger pixel area hence better light collecting capacity for a given aperture compared to Nikon P300.
Below you can see the P300 and XQ1 sensor size comparison.
Sensor Size and Resolution Comparison image of Nikon P300 and Fujifilm XQ1 Cameras
As seen above, Fujifilm XQ1 has a 2.1x Larger sensor area than Nikon P300. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.